Phrase origin

In Reply to: Phrase origin posted by Nigel Hughes on December 22, 2003

: Hi,

: Does anybody know the origin and meaning of the phrase "off my own bat"?

: Cheers and Merry Christmas,
: Nigel.

Here's the explanation that I've found.
To do something 'off your own bat' means to do something on your own initiative, without help, or even without permission. Why 'bat'? This is said to be an analogy with cricket, where a batsman scores runs 'off his own bat'.